Glasnik Matematicki, Vol. 44, No.2 (2009), 447-455.

ON SOME FUNCTIONAL EQUATIONS ON STANDARD OPERATOR ALGEBRAS

Irena Kosi-Ulbl and Joso Vukman

Faculty of Mechanical Engineering, University of Maribor, Smetanova ul. 17, Maribor, Slovenia
e-mail: irena.kosi@uni-mb.si

Department of Mathematics and Computer Science, FNM, University of Maribor, Koroska 160, Maribor, Slovenia
e-mail: joso.vukman@uni-mb.si


Abstract.   The main purpose of this paper is to prove the following result. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators on X, let A(X) subset L(X) be a standard operator algebra, and let T : A(X) → L(X) be an additive mapping satisfying the relation T(A2n+1) = ∑i=12n+1 (-1)i+1 Ai-1 T(A) A2n+1-i, for all A in A(X) and some fixed integer n ≥ 1. In this case T\ is of the form T(A) = AB + BA, for all A in A(X) and some fixed B in L(X). In particular, T is continuous.

2000 Mathematics Subject Classification.   46K15, 39B05.

Key words and phrases.   Prime ring, semiprime ring, Banach space, standard operator algebra.


Full text (PDF) (free access)

DOI: 10.3336/gm.44.2.11


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